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25 //
26 //
27 //
28 // Author: Alexander Bagulya
29 // 11 March 2012
30 // on the base of G4LivermoreComptonModel
31 //
32 // History:
33 // --------
34 // 18 Apr 2009 V Ivanchenko Cleanup initialisation and generation of secondaries:
35 // - apply internal high-energy limit only in constructor
36 // - do not apply low-energy limit (default is 0)
37 // - remove GetMeanFreePath method and table
38 // - added protection against numerical problem in energy sampling
39 // - use G4ElementSelector
40 // 26 Dec 2010 V Ivanchenko Load data tables only once to avoid memory leak
41
42 #include "G4LivermoreComptonModel.hh"
43
44 #include "G4AtomicShell.hh"
45 #include "G4AutoLock.hh"
46 #include "G4DopplerProfile.hh"
47 #include "G4Electron.hh"
48 #include "G4Exp.hh"
49 #include "G4Log.hh"
50 #include "G4LossTableManager.hh"
51 #include "G4ParticleChangeForGamma.hh"
52 #include "G4PhysicalConstants.hh"
53 #include "G4ShellData.hh"
54 #include "G4SystemOfUnits.hh"
55 #include "G4VAtomDeexcitation.hh"
56
57 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
58
59 namespace
60 {
61 G4Mutex LivermoreComptonModelMutex = G4MUTEX_INITIALIZER;
62 }
63 using namespace std;
64
65 G4PhysicsFreeVector* G4LivermoreComptonModel::data[] = {nullptr};
66 G4ShellData* G4LivermoreComptonModel::shellData = nullptr;
67 G4DopplerProfile* G4LivermoreComptonModel::profileData = nullptr;
68 G4String G4LivermoreComptonModel::gDataDirectory = "";
69
70 static const G4double ln10 = G4Log(10.);
71
72 G4LivermoreComptonModel::G4LivermoreComptonModel(const G4ParticleDefinition*, const G4String& nam)
73 : G4VEmModel(nam)
74 {
75 fParticleChange = nullptr;
76 verboseLevel = 1;
77 // Verbosity scale:
78 // 0 = nothing
79 // 1 = warning for energy non-conservation
80 // 2 = details of energy budget
81 // 3 = calculation of cross sections, file openings, sampling of atoms
82 // 4 = entering in methods
83
84 if (verboseLevel > 1) {
85 G4cout << "Livermore Compton model is constructed " << G4endl;
86 }
87
88 // Mark this model as "applicable" for atomic deexcitation
89 SetDeexcitationFlag(true);
90
91 fParticleChange = nullptr;
92 fAtomDeexcitation = nullptr;
93 }
94
95 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
96
97 G4LivermoreComptonModel::~G4LivermoreComptonModel()
98 {
99 if (IsMaster()) {
100 delete shellData;
101 shellData = nullptr;
102 delete profileData;
103 profileData = nullptr;
104 for (G4int i = 0; i <= maxZ; ++i) {
105 if (data[i]) {
106 delete data[i];
107 data[i] = nullptr;
108 }
109 }
110 }
111 }
112
113 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
114
115 void G4LivermoreComptonModel::Initialise(const G4ParticleDefinition* particle,
116 const G4DataVector& cuts)
117 {
118 if (verboseLevel > 1) {
119 G4cout << "Calling G4LivermoreComptonModel::Initialise()" << G4endl;
120 }
121
122 // Initialise element selector
123 if (IsMaster()) {
124 // Initialise element selector
125 InitialiseElementSelectors(particle, cuts);
126
127 // Access to elements
128 const G4ElementTable* elemTable = G4Element::GetElementTable();
129 size_t numElems = (*elemTable).size();
130 for (size_t ie = 0; ie < numElems; ++ie) {
131 const G4Element* elem = (*elemTable)[ie];
132 const G4int Z = std::min(maxZ, elem->GetZasInt());
133 if (data[Z] == nullptr) {
134 ReadData(Z);
135 }
136 }
137
138 // For Doppler broadening
139 if (shellData == nullptr) {
140 shellData = new G4ShellData();
141 shellData->SetOccupancyData();
142 G4String file = "/doppler/shell-doppler";
143 shellData->LoadData(file);
144 }
145 if (profileData == nullptr) {
146 profileData = new G4DopplerProfile();
147 }
148 }
149
150 if (verboseLevel > 2) {
151 G4cout << "Loaded cross section files" << G4endl;
152 }
153
154 if (verboseLevel > 1) {
155 G4cout << "G4LivermoreComptonModel is initialized " << G4endl
156 << "Energy range: " << LowEnergyLimit() / eV << " eV - " << HighEnergyLimit() / GeV
157 << " GeV" << G4endl;
158 }
159 //
160 if (isInitialised) {
161 return;
162 }
163
164 fParticleChange = GetParticleChangeForGamma();
165 fAtomDeexcitation = G4LossTableManager::Instance()->AtomDeexcitation();
166 isInitialised = true;
167 }
168
169 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
170
171 void G4LivermoreComptonModel::InitialiseLocal(const G4ParticleDefinition*, G4VEmModel* masterModel)
172 {
173 SetElementSelectors(masterModel->GetElementSelectors());
174 }
175
176 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
177
178 const G4String& G4LivermoreComptonModel::FindDirectoryPath()
179 {
180 // no check in this method - environment variable is check by utility
181 if (gDataDirectory.empty()) {
182 auto param = G4EmParameters::Instance();
183 std::ostringstream ost;
184 if (param->LivermoreDataDir() == "livermore") {
185 ost << param->GetDirLEDATA() << "/livermore/comp/";
186 }
187 else {
188 ost << param->GetDirLEDATA() << "/epics2017/comp/";
189 }
190 gDataDirectory = ost.str();
191 }
192 return gDataDirectory;
193 }
194
195 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
196
197 void G4LivermoreComptonModel::ReadData(const G4int ZZ)
198 {
199 if (verboseLevel > 1) {
200 G4cout << "G4LivermoreComptonModel::ReadData()" << G4endl;
201 }
202 const G4int Z = std::min(ZZ, maxZ);
203
204 if (data[Z] != nullptr) {
205 return;
206 }
207
208 data[Z] = new G4PhysicsFreeVector();
209
210 std::ostringstream ost;
211 ost << FindDirectoryPath() << "ce-cs-" << Z << ".dat";
212
213 std::ifstream fin(ost.str().c_str());
214
215 if (!fin.is_open()) {
216 G4ExceptionDescription ed;
217 ed << "G4LivermoreComptonModel data file <" << ost.str().c_str() << "> is not opened!"
218 << G4endl;
219 G4Exception("G4LivermoreComptonModel::ReadData()", "em0003", FatalException, ed,
220 "G4LEDATA version should be G4EMLOW8.0 or later");
221 return;
222 }
223 else {
224 if (verboseLevel > 3) {
225 G4cout << "File " << ost.str() << " is opened by G4LivermoreComptonModel" << G4endl;
226 }
227 data[Z]->Retrieve(fin, true);
228 data[Z]->ScaleVector(MeV, MeV * barn);
229 }
230 fin.close();
231 }
232
233 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
234
235 G4double G4LivermoreComptonModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
236 G4double GammaEnergy, G4double Z,
237 G4double, G4double, G4double)
238 {
239 if (verboseLevel > 3) {
240 G4cout << "G4LivermoreComptonModel::ComputeCrossSectionPerAtom()" << G4endl;
241 }
242 G4double cs = 0.0;
243
244 if (GammaEnergy < LowEnergyLimit()) {
245 return 0.0;
246 }
247
248 G4int intZ = G4lrint(Z);
249 if (intZ < 1 || intZ > maxZ) {
250 return cs;
251 }
252
253 G4PhysicsFreeVector* pv = data[intZ];
254
255 // if element was not initialised
256 // do initialisation safely for MT mode
257 if (pv == nullptr) {
258 InitialiseForElement(nullptr, intZ);
259 pv = data[intZ];
260 if (pv == nullptr) {
261 return cs;
262 }
263 }
264
265 auto n = G4int(pv->GetVectorLength() - 1);
266 G4double e1 = pv->Energy(0);
267 G4double e2 = pv->Energy(n);
268
269 if (GammaEnergy <= e1) {
270 cs = GammaEnergy / (e1 * e1) * pv->Value(e1);
271 }
272 else if (GammaEnergy <= e2) {
273 cs = pv->Value(GammaEnergy) / GammaEnergy;
274 }
275 else if (GammaEnergy > e2) {
276 cs = pv->Value(e2) / GammaEnergy;
277 }
278
279 return cs;
280 }
281
282 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
283
284 void G4LivermoreComptonModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
285 const G4MaterialCutsCouple* couple,
286 const G4DynamicParticle* aDynamicGamma, G4double,
287 G4double)
288 {
289 // The scattered gamma energy is sampled according to Klein - Nishina
290 // formula then accepted or rejected depending on the Scattering Function
291 // multiplied by factor from Klein - Nishina formula.
292 // Expression of the angular distribution as Klein Nishina
293 // angular and energy distribution and Scattering fuctions is taken from
294 // D. E. Cullen "A simple model of photon transport" Nucl. Instr. Meth.
295 // Phys. Res. B 101 (1995). Method of sampling with form factors is different
296 // data are interpolated while in the article they are fitted.
297 // Reference to the article is from J. Stepanek New Photon, Positron
298 // and Electron Interaction Data for GEANT in Energy Range from 1 eV to 10
299 // TeV (draft).
300 // The random number techniques of Butcher & Messel are used
301 // (Nucl Phys 20(1960),15).
302
303 G4double photonEnergy0 = aDynamicGamma->GetKineticEnergy();
304
305 if (verboseLevel > 3) {
306 G4cout << "G4LivermoreComptonModel::SampleSecondaries() E(MeV)= " << photonEnergy0 / MeV
307 << " in " << couple->GetMaterial()->GetName() << G4endl;
308 }
309
310 // do nothing below the threshold
311 // should never get here because the XS is zero below the limit
312 if (photonEnergy0 < LowEnergyLimit()) return;
313
314 G4double e0m = photonEnergy0 / electron_mass_c2;
315 G4ParticleMomentum photonDirection0 = aDynamicGamma->GetMomentumDirection();
316
317 // Select randomly one element in the current material
318 const G4ParticleDefinition* particle = aDynamicGamma->GetDefinition();
319 const G4Element* elm = SelectRandomAtom(couple, particle, photonEnergy0);
320
321 G4int Z = elm->GetZasInt();
322
323 G4double epsilon0Local = 1. / (1. + 2. * e0m);
324 G4double epsilon0Sq = epsilon0Local * epsilon0Local;
325 G4double alpha1 = -G4Log(epsilon0Local);
326 G4double alpha2 = 0.5 * (1. - epsilon0Sq);
327
328 G4double wlPhoton = h_Planck * c_light / photonEnergy0;
329
330 // Sample the energy of the scattered photon
331 G4double epsilon;
332 G4double epsilonSq;
333 G4double oneCosT;
334 G4double sinT2;
335 G4double gReject;
336
337 if (verboseLevel > 3) {
338 G4cout << "Started loop to sample gamma energy" << G4endl;
339 }
340
341 do {
342 if (alpha1 / (alpha1 + alpha2) > G4UniformRand()) {
343 epsilon = G4Exp(-alpha1 * G4UniformRand());
344 epsilonSq = epsilon * epsilon;
345 }
346 else {
347 epsilonSq = epsilon0Sq + (1. - epsilon0Sq) * G4UniformRand();
348 epsilon = std::sqrt(epsilonSq);
349 }
350
351 oneCosT = (1. - epsilon) / (epsilon * e0m);
352 sinT2 = oneCosT * (2. - oneCosT);
353 G4double x = std::sqrt(oneCosT / 2.) * cm / wlPhoton;
354 G4double scatteringFunction = ComputeScatteringFunction(x, Z);
355 gReject = (1. - epsilon * sinT2 / (1. + epsilonSq)) * scatteringFunction;
356
357 } while (gReject < G4UniformRand() * Z);
358
359 G4double cosTheta = 1. - oneCosT;
360 G4double sinTheta = std::sqrt(sinT2);
361 G4double phi = twopi * G4UniformRand();
362 G4double dirx = sinTheta * std::cos(phi);
363 G4double diry = sinTheta * std::sin(phi);
364 G4double dirz = cosTheta;
365
366 // Doppler broadening - Method based on:
367 // Y. Namito, S. Ban and H. Hirayama,
368 // "Implementation of the Doppler Broadening of a Compton-Scattered Photon
369 // into the EGS4 Code", NIM A 349, pp. 489-494, 1994
370
371 // Maximum number of sampling iterations
372 static G4int maxDopplerIterations = 1000;
373 G4double bindingE = 0.;
374 G4double photonEoriginal = epsilon * photonEnergy0;
375 G4double photonE = -1.;
376 G4int iteration = 0;
377 G4double eMax = photonEnergy0;
378
379 G4int shellIdx = 0;
380
381 if (verboseLevel > 3) {
382 G4cout << "Started loop to sample broading" << G4endl;
383 }
384
385 do {
386 ++iteration;
387 // Select shell based on shell occupancy
388 shellIdx = shellData->SelectRandomShell(Z);
389 bindingE = shellData->BindingEnergy(Z, shellIdx);
390
391 if (verboseLevel > 3) {
392 G4cout << "Shell ID= " << shellIdx << " Ebind(keV)= " << bindingE / keV << G4endl;
393 }
394
395 eMax = photonEnergy0 - bindingE;
396
397 // Randomly sample bound electron momentum
398 // (memento: the data set is in Atomic Units)
399 G4double pSample = profileData->RandomSelectMomentum(Z, shellIdx);
400 if (verboseLevel > 3) {
401 G4cout << "pSample= " << pSample << G4endl;
402 }
403 // Rescale from atomic units
404 G4double pDoppler = pSample * fine_structure_const;
405 G4double pDoppler2 = pDoppler * pDoppler;
406 G4double var2 = 1. + oneCosT * e0m;
407 G4double var3 = var2 * var2 - pDoppler2;
408 G4double var4 = var2 - pDoppler2 * cosTheta;
409 G4double var = var4 * var4 - var3 + pDoppler2 * var3;
410 if (var > 0.) {
411 G4double varSqrt = std::sqrt(var);
412 G4double scale = photonEnergy0 / var3;
413 // Random select either root
414 if (G4UniformRand() < 0.5) {
415 photonE = (var4 - varSqrt) * scale;
416 }
417 else {
418 photonE = (var4 + varSqrt) * scale;
419 }
420 }
421 else {
422 photonE = -1.;
423 }
424 } while (iteration <= maxDopplerIterations && photonE > eMax);
425
426 // End of recalculation of photon energy with Doppler broadening
427 // Revert to original if maximum number of iterations threshold
428 // has been reached
429 if (iteration >= maxDopplerIterations) {
430 photonE = photonEoriginal;
431 bindingE = 0.;
432 }
433
434 // Update G4VParticleChange for the scattered photon
435 G4ThreeVector photonDirection1(dirx, diry, dirz);
436 photonDirection1.rotateUz(photonDirection0);
437 fParticleChange->ProposeMomentumDirection(photonDirection1);
438
439 G4double photonEnergy1 = photonE;
440
441 if (photonEnergy1 > 0.) {
442 fParticleChange->SetProposedKineticEnergy(photonEnergy1);
443 }
444 else {
445 // photon absorbed
446 photonEnergy1 = 0.;
447 fParticleChange->SetProposedKineticEnergy(0.);
448 fParticleChange->ProposeTrackStatus(fStopAndKill);
449 fParticleChange->ProposeLocalEnergyDeposit(photonEnergy0);
450 return;
451 }
452
453 // Kinematics of the scattered electron
454 G4double eKineticEnergy = photonEnergy0 - photonEnergy1 - bindingE;
455
456 // protection against negative final energy: no e- is created
457 if (eKineticEnergy < 0.0) {
458 fParticleChange->ProposeLocalEnergyDeposit(photonEnergy0 - photonEnergy1);
459 return;
460 }
461
462 G4double eTotalEnergy = eKineticEnergy + electron_mass_c2;
463
464 G4double electronE = photonEnergy0 * (1. - epsilon) + electron_mass_c2;
465 G4double electronP2 = electronE * electronE - electron_mass_c2 * electron_mass_c2;
466 G4double sinThetaE = -1.;
467 G4double cosThetaE = 0.;
468 if (electronP2 > 0.) {
469 cosThetaE = (eTotalEnergy + photonEnergy1) * (1. - epsilon) / std::sqrt(electronP2);
470 sinThetaE = -1. * sqrt(1. - cosThetaE * cosThetaE);
471 }
472
473 G4double eDirX = sinThetaE * std::cos(phi);
474 G4double eDirY = sinThetaE * std::sin(phi);
475 G4double eDirZ = cosThetaE;
476
477 G4ThreeVector eDirection(eDirX, eDirY, eDirZ);
478 eDirection.rotateUz(photonDirection0);
479 auto dp = new G4DynamicParticle(G4Electron::Electron(), eDirection, eKineticEnergy);
480 fvect->push_back(dp);
481
482 // sample deexcitation
483 if (verboseLevel > 3) {
484 G4cout << "Started atomic de-excitation " << fAtomDeexcitation << G4endl;
485 }
486
487 if (nullptr != fAtomDeexcitation && iteration < maxDopplerIterations) {
488 G4int index = couple->GetIndex();
489 if (fAtomDeexcitation->CheckDeexcitationActiveRegion(index)) {
490 size_t nbefore = fvect->size();
491 auto as = G4AtomicShellEnumerator(shellIdx);
492 const G4AtomicShell* shell = fAtomDeexcitation->GetAtomicShell(Z, as);
493 fAtomDeexcitation->GenerateParticles(fvect, shell, Z, index);
494 size_t nafter = fvect->size();
495 if (nafter > nbefore) {
496 for (size_t i = nbefore; i < nafter; ++i) {
497 // Check if there is enough residual energy
498 if (bindingE >= ((*fvect)[i])->GetKineticEnergy()) {
499 // Ok, this is a valid secondary: keep it
500 bindingE -= ((*fvect)[i])->GetKineticEnergy();
501 }
502 else {
503 // Invalid secondary: not enough energy to create it!
504 // Keep its energy in the local deposit
505 delete (*fvect)[i];
506 (*fvect)[i] = nullptr;
507 }
508 }
509 }
510 }
511 }
512 bindingE = std::max(bindingE, 0.0);
513 fParticleChange->ProposeLocalEnergyDeposit(bindingE);
514 }
515
516 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
517
518 G4double G4LivermoreComptonModel::ComputeScatteringFunction(G4double x, G4int Z)
519 {
520 G4double value = Z;
521 if (x <= ScatFuncFitParam[Z][3]) {
522 G4double lgq = G4Log(x) / ln10;
523
524 if (lgq < ScatFuncFitParam[Z][1]) {
525 value = ScatFuncFitParam[Z][4] + lgq * ScatFuncFitParam[Z][5];
526 }
527 else if (lgq >= ScatFuncFitParam[Z][1] && lgq < ScatFuncFitParam[Z][2]) {
528 value = ScatFuncFitParam[Z][6]
529 + lgq
530 * (ScatFuncFitParam[Z][7]
531 + lgq
532 * (ScatFuncFitParam[Z][8]
533 + lgq * (ScatFuncFitParam[Z][9] + lgq * ScatFuncFitParam[Z][10])));
534 }
535 else {
536 value = ScatFuncFitParam[Z][11]
537 + lgq
538 * (ScatFuncFitParam[Z][12]
539 + lgq
540 * (ScatFuncFitParam[Z][13]
541 + lgq * (ScatFuncFitParam[Z][14] + lgq * ScatFuncFitParam[Z][15])));
542 }
543 value = G4Exp(value * ln10);
544 }
545 // G4cout << " value= " << value << G4endl;
546 return value;
547 }
548
549 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
550
551 void G4LivermoreComptonModel::InitialiseForElement(const G4ParticleDefinition*, G4int Z)
552 {
553 G4AutoLock l(&LivermoreComptonModelMutex);
554 if (data[Z] == nullptr) {
555 ReadData(Z);
556 }
557 l.unlock();
558 }
559
560 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
561
562 // Fitting data to compute scattering function based on EPICS2017
563 const G4double G4LivermoreComptonModel::ScatFuncFitParam[101][16] = {
564 {0, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.},
565 {1, 6.000000000e+00, 7.087999300e+00, 1.499680000e+08, -1.435559123e+01, 2.000000043e+00,
566 -3.925518125e+02, 2.434944521e+02, -5.784393623e+01, 6.160181204e+00, -2.461326602e-01,
567 -1.649463594e+03, 8.121933215e+02, -1.498313316e+02, 1.227279742e+01, -3.765996345e-01},
568 {2, 6.000000000e+00, 7.199000403e+00, 2.500350000e+08, -1.430103027e+01, 2.000000041e+00,
569 3.574019365e+02, -1.978574937e+02, 3.971327838e+01, -3.443224867e+00, 1.091825227e-01,
570 -4.009960832e+02, 1.575831469e+02, -2.174763446e+01, 1.185163045e+00, -1.814503741e-02},
571 {3, 6.000000000e+00, 7.301000136e+00, 3.999450000e+08, -1.357675458e+01, 2.000000074e+00,
572 7.051635443e+02, -4.223841786e+02, 9.318729225e+01, -9.002642767e+00, 3.220625771e-01,
573 1.524679907e+03, -7.851479582e+02, 1.509941052e+02, -1.285477984e+01, 4.089348830e-01},
574 {4, 6.000000000e+00, 7.349500202e+00, 5.000350000e+08, -1.375202671e+01, 1.999999994e+00,
575 -1.832909604e+02, 1.193997722e+02, -3.034328318e+01, 3.471545044e+00, -1.484222463e-01,
576 1.397476657e+03, -7.026416933e+02, 1.320720559e+02, -1.099824430e+01, 3.424610532e-01},
577 {5, 6.000000000e+00, 7.388999972e+00, 5.997910000e+08, -1.380548571e+01, 2.000000004e+00,
578 -2.334197545e+02, 1.467013466e+02, -3.574851109e+01, 3.925047955e+00, -1.616186492e-01,
579 6.784713308e+02, -3.419562074e+02, 6.433945831e+01, -5.354244209e+00, 1.663784966e-01},
580 {6, 6.000000000e+00, 7.422500001e+00, 6.998420000e+08, -1.388639003e+01, 1.999999863e+00,
581 -2.460254935e+02, 1.516613633e+02, -3.622024219e+01, 3.900099543e+00, -1.576557530e-01,
582 -1.610185428e+02, 7.010907070e+01, -1.142375397e+01, 8.303365180e-01, -2.273786010e-02},
583 {7, 6.000000000e+00, 7.451499931e+00, 7.998340000e+08, -1.388605429e+01, 1.999999612e+00,
584 -3.054540719e+02, 1.877740247e+02, -4.440273010e+01, 4.718886370e+00, -1.881615004e-01,
585 -2.263864349e+02, 1.017885461e+02, -1.716982752e+01, 1.292954622e+00, -3.668301946e-02},
586 {8, 6.000000000e+00, 7.451499931e+00, 7.998340000e+08, -1.395860675e+01, 1.999999906e+00,
587 -3.877174895e+02, 2.345831969e+02, -5.431822300e+01, 5.643262324e+00, -2.200840540e-01,
588 -7.949384302e+02, 3.757293602e+02, -6.661741851e+01, 5.256265086e+00, -1.556986777e-01},
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739 {59, 6.000000000e+00, 7.849500202e+00, 5.000350000e+09, -1.293554133e+01, 1.999999890e+00,
740 1.214691988e+02, -8.336119630e+01, 1.996468944e+01, -2.032283439e+00, 7.562254632e-02,
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745 {61, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.295078139e+01, 1.999999905e+00,
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749 1.203145109e+02, -8.212556537e+01, 1.956606386e+01, -1.981212240e+00, 7.333626288e-02,
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751 {63, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.296657573e+01, 1.999999918e+00,
752 1.212159597e+02, -8.256559477e+01, 1.964122173e+01, -1.986442056e+00, 7.345564343e-02,
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755 1.689382403e+02, -1.099987696e+02, 2.551961464e+01, -2.543234152e+00, 9.313568005e-02,
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757 {65, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.299139910e+01, 1.999999880e+00,
758 1.724155378e+02, -1.120798437e+02, 2.598264738e+01, -2.588807295e+00, 9.481417896e-02,
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760 {66, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.298716240e+01, 1.999999941e+00,
761 1.286079419e+02, -8.646296410e+01, 2.039801258e+01, -2.050839207e+00, 7.549033493e-02,
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763 {67, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.299567846e+01, 1.999999971e+00,
764 1.182799697e+02, -8.043389241e+01, 1.908027783e+01, -1.923209794e+00, 7.087268462e-02,
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766 {68, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.300436459e+01, 1.999999966e+00,
767 1.150510247e+02, -7.859576077e+01, 1.868688175e+01, -1.885844183e+00, 6.954765052e-02,
768 -2.457555063e+02, 1.007538481e+02, -1.536692833e+01, 1.041070997e+00, -2.643279207e-02},
769 {69, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.300877391e+01, 2.000000000e+00,
770 1.266280406e+02, -8.514491730e+01, 2.007089332e+01, -2.015475088e+00, 7.409191965e-02,
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772 {70, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.301772826e+01, 1.999999912e+00,
773 1.224253568e+02, -8.281395858e+01, 1.958609738e+01, -1.970785167e+00, 7.255458061e-02,
774 -2.488808342e+02, 1.018569466e+02, -1.550601866e+01, 1.048325396e+00, -2.655661748e-02},
775 {71, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.303151733e+01, 2.000000051e+00,
776 1.862181262e+02, -1.199038630e+02, 2.763107534e+01, -2.742586837e+00, 1.001956495e-01,
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778 {72, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.304575796e+01, 2.000000081e+00,
779 2.297759959e+02, -1.448485621e+02, 3.295877082e+01, -3.245850428e+00, 1.179456377e-01,
780 -2.282155654e+02, 9.249921555e+01, -1.392266984e+01, 9.297052139e-01, -2.323558576e-02},
781 {73, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.306048022e+01, 1.999999910e+00,
782 2.646909006e+02, -1.647716545e+02, 3.719903613e+01, -3.645113853e+00, 1.319890617e-01,
783 -2.165150972e+02, 8.722660467e+01, -1.303415548e+01, 8.633600348e-01, -2.138300143e-02},
784 {74, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.308092196e+01, 2.000000008e+00,
785 2.251239174e+02, -1.414731209e+02, 3.206048507e+01, -3.142433101e+00, 1.135971917e-01,
786 -2.070173544e+02, 8.296725365e+01, -1.231986936e+01, 8.102887128e-01, -1.990853407e-02},
787 {75, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.309151488e+01, 1.999999984e+00,
788 2.627532736e+02, -1.629008146e+02, 3.661592385e+01, -3.571257833e+00, 1.286871297e-01,
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790 {76, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.310790581e+01, 2.000000068e+00,
791 2.644549626e+02, -1.637369900e+02, 3.675734857e+01, -3.580665992e+00, 1.288721975e-01,
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793 {77, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.311918599e+01, 1.999999933e+00,
794 2.677629012e+02, -1.650589135e+02, 3.690999414e+01, -3.582378706e+00, 1.284763849e-01,
795 -1.584140848e+02, 6.122430396e+01, -8.680876005e+00, 5.402879020e-01, -1.241386995e-02},
796 {78, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.319382006e+01, 2.000000009e+00,
797 2.420702029e+02, -1.484461630e+02, 3.292288306e+01, -3.162757529e+00, 1.121487556e-01,
798 -1.319886050e+02, 4.940494114e+01, -6.702740089e+00, 3.934770465e-01, -8.336673895e-03},
799 {79, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.320760814e+01, 1.999999969e+00,
800 2.346714957e+02, -1.439356552e+02, 3.189416251e+01, -3.059071523e+00, 1.082595858e-01,
801 -1.130109430e+02, 4.093029258e+01, -5.286747014e+00, 2.885753389e-01, -5.428939868e-03},
802 {80, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.316115147e+01, 2.000000093e+00,
803 2.747370538e+02, -1.689673404e+02, 3.771696324e+01, -3.655841153e+00, 1.309852214e-01,
804 -9.001823908e+01, 3.066094857e+01, -3.570459523e+00, 1.613797666e-01, -1.901561361e-03},
805 {81, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.313667715e+01, 2.000000002e+00,
806 3.142563781e+02, -1.916613838e+02, 4.259167223e+01, -4.119713271e+00, 1.474792530e-01,
807 -7.642731867e+01, 2.462410146e+01, -2.566977318e+00, 8.741068396e-02, 1.388590928e-04},
808 {82, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.314266674e+01, 1.999999876e+00,
809 3.509258060e+02, -2.125470710e+02, 4.702461797e+01, -4.535380912e+00, 1.620138781e-01,
810 -5.173355302e+01, 1.362015056e+01, -7.321282362e-01, -4.826261322e-02, 3.892879264e-03},
811 {83, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.315490164e+01, 1.999999944e+00,
812 3.399729483e+02, -2.056319770e+02, 4.539614689e+01, -4.366195994e+00, 1.554792165e-01,
813 -4.131443229e+01, 8.986236911e+00, 3.924628986e-02, -1.052060828e-01, 5.466043586e-03},
814 {84, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.316749062e+01, 1.999999920e+00,
815 3.640602841e+02, -2.190164327e+02, 4.815603439e+01, -4.616573783e+00, 1.639147626e-01,
816 -3.256862965e+01, 5.115606198e+00, 6.800853161e-01, -1.522315744e-01, 6.756786448e-03},
817 {85, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.318045630e+01, 2.000000044e+00,
818 3.766488275e+02, -2.257321142e+02, 4.947300991e+01, -4.728919006e+00, 1.674240471e-01,
819 -2.300947210e+01, 8.615223509e-01, 1.388425307e+00, -2.045157608e-01, 8.200511055e-03},
820 {86, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.319382005e+01, 2.000000006e+00,
821 3.443622947e+02, -2.064342780e+02, 4.516044966e+01, -4.302253084e+00, 1.516667044e-01,
822 -5.399039282e+00, -7.002814559e+00, 2.702516748e+00, -3.018766003e-01, 1.089953798e-02},
823 {87, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.291364147e+01, 2.000000217e+00,
824 -3.706791591e+01, 1.118013187e+01, -1.057728859e+00, 3.312859839e-02, -3.138341244e-06,
825 -3.451314336e+00, -7.779254134e+00, 2.816269849e+00, -3.090776388e-01, 1.106424389e-02},
826 {88, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.284163724e+01, 1.999999954e+00,
827 6.125934670e+01, -4.855548659e+01, 1.248551381e+01, -1.323304763e+00, 5.060744172e-02,
828 -6.021643455e+00, -6.580234329e+00, 2.607440108e+00, -2.929625239e-01, 1.059951856e-02},
829 {89, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.285387248e+01, 2.000000090e+00,
830 1.350863292e+02, -9.126618691e+01, 2.169932948e+01, -2.201947573e+00, 8.186860720e-02,
831 1.937135880e+01, -1.787129621e+01, 4.485878662e+00, -4.315325969e-01, 1.442445798e-02},
832 {90, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.286966604e+01, 1.999999970e+00,
833 1.784388998e+02, -1.161623817e+02, 2.702376618e+01, -2.704797298e+00, 9.957279361e-02,
834 2.216057166e+01, -1.904990091e+01, 4.671627339e+00, -4.444534802e-01, 1.475921763e-02},
835 {91, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.287289489e+01, 1.999999951e+00,
836 1.368355213e+02, -9.179790820e+01, 2.169910915e+01, -2.190249857e+00, 8.102241740e-02,
837 4.516580666e+00, -1.118102949e+01, 3.357662550e+00, -3.470694353e-01, 1.205639951e-02},
838 {92, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.287942629e+01, 2.000000032e+00,
839 1.427130850e+02, -9.499714618e+01, 2.234475916e+01, -2.247599931e+00, 8.291713193e-02,
840 1.341991149e+01, -1.518503354e+01, 4.030838171e+00, -3.972060658e-01, 1.345248084e-02},
841 {93, 6.000000000e+00, 8.000000000e+00, 1.000000000e+10, -1.288605524e+01, 1.999999761e+00,
842 2.341801100e+01, -2.506119713e+01, 7.023029272e+00, -7.610742531e-01, 2.903245750e-02,
843 -3.575331738e+01, 7.276302226e+00, 1.906771859e-01, -1.059475755e-01, 5.184029625e-03},
844 {94, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.288272835e+01, 1.999999941e+00,
845 1.287618322e+02, -8.721780968e+01, 2.073255323e+01, -2.100572716e+00, 7.794295578e-02,
846 -2.307262580e+01, 1.113132278e+00, 1.305250601e+00, -1.948949139e-01, 7.829116438e-03},
847 {95, 6.000000000e+00, 7.951499931e+00, 7.998340000e+09, -1.288940956e+01, 1.999999880e+00,
848 1.334821220e+02, -8.985337775e+01, 2.127928526e+01, -2.150628571e+00, 7.965294640e-02,
849 -3.518662723e+01, 6.514543434e+00, 4.030862442e-01, -1.279850170e-01, 5.970168353e-03},
850 {96, 6.000000000e+00, 8.000000000e+00, 1.000000000e+10, -1.290553004e+01, 2.000000198e+00,
851 4.545581472e+01, -3.771304300e+01, 9.729129321e+00, -1.017037014e+00, 3.807733199e-02,
852 -4.973805034e+01, 1.342335334e+01, -8.221139917e-01, -3.176841835e-02, 3.146810827e-03},
853 {97, 6.000000000e+00, 8.000000000e+00, 1.000000000e+10, -1.291150963e+01, 2.000000019e+00,
854 4.689042092e+01, -3.843347264e+01, 9.859294531e+00, -1.027014690e+00, 3.834833665e-02,
855 -4.657434145e+01, 1.204637835e+01, -5.982449163e-01, -4.786919243e-02, 3.579251285e-03},
856 {98, 6.000000000e+00, 8.000000000e+00, 1.000000000e+10, -1.290833198e+01, 1.999999824e+00,
857 1.337584189e+01, -1.907284620e+01, 5.691614909e+00, -6.307838734e-01, 2.430868142e-02,
858 -5.573362773e+01, 1.615667599e+01, -1.288960621e+00, 3.655033732e-03, 2.140047522e-03},
859 {99, 6.000000000e+00, 8.000000000e+00, 1.000000000e+10, -1.291435263e+01, 1.999999988e+00,
860 1.376201293e+01, -1.919251815e+01, 5.693799461e+00, -6.287500644e-01, 2.416045199e-02,
861 -4.914211254e+01, 1.314247998e+01, -7.739336035e-01, -3.530513333e-02, 3.241293077e-03},
862 {100, 6.000000000e+00, 8.000000000e+00, 1.000000000e+10, -1.292045700e+01, 2.000000004e+00,
863 1.277081775e+01, -1.854047224e+01, 5.534680382e+00, -6.118054153e-01, 2.349768815e-02,
864 -5.074293980e+01, 1.383260974e+01, -8.858904786e-01, -2.718885953e-02, 3.019620454e-03}};
865 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
866